$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 6x + 7$ and $ KL = 9x - 2$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {6x + 7} = {9x - 2}$ Solve for $x$ $ -3x = -9$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 6({3}) + 7$ $ KL = 9({3}) - 2$ $ JK = 18 + 7$ $ KL = 27 - 2$ $ JK = 25$ $ KL = 25$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {25} + {25}$ $ JL = 50$